Screen for projection display in which the light is uniformly transmitted throughout the screen

ABSTRACT

A screen for a projection display is provided. The screen includes a Fresnel lens sheet which converges light emitted from a light source, and a lenticular lens sheet which disperses in a horizontal direction the light transmitted by the Fresnel lens sheet. The Fresnel lens sheet includes a first Fresnel lens on one surface and a second Fresnel lens on an opposite surface.

BACKGROUND OF THE INVENTION

This application claims the priority of Korean Patent Application No.2003-48428, filed on Jul. 15, 2003, in the Korean Intellectual PropertyOffice, the disclosure of which is incorporated herein in its entiretyby reference.

1. Field of the Invention

The present invention relates to a screen for a projection display and,more particularly, to a projection display with a high definition view,slim structure and a large screen in which the light is uniformlytransmitted throughout the screen even when an incident angle of lightemitted from an optical projection system onto the screen is differentdepending on the position on the screen to which the light istransmitted.

2. Description of the Related Art

Referring to FIG. 1, a projection screen usually includes a Fresnel lenssheet 10 which collects light flux projected by an optical projectionsystem toward a viewer, and a lenticular lens sheet 20 which dispersesthe light output from the Fresnel lens sheet 10 at a predetermined anglewith respect to a horizontal direction of the screen, to widen a viewingangle.

A lenticular lens 20 a is formed on an incident surface of thelenticular lens sheet 20 to disperse light in the horizontal direction.A black stripe 20 b is formed on an exit surface of the lenticular lenssheet 20 to absorb the diverging light and to block the externallyincident light, thereby increasing a contrast ratio.

Recently, projection displays having a large screen, a high definitionview, and a slim structure have been researched and developed. In FIG.2A, an optical projection system 25 is disposed at the same level as acenter of the Fresnel lens sheet 10, with a plane incident surface 10 aand an exit surface 10 b. With this arrangement, it is necessary todecrease the height of a quadrangular pyramid of a light flux outputfrom the optical projection system 25 to make the projection displaysslim. However, when the optical projection system 25 is disposed at thesame level as the center of the screen, the light flux output from theoptical projection system 25 cannot be decreased to an optimal height ofthe quadrangular pyramid.

To solve this problem, the optical projection system 25 is disposedobliquely below the screen, as shown in FIG. 2B. However, in this case,the light loss increases due to a reflection at a peripheral portion ofthe Fresnel lens sheet 10, and the brightness at the peripheral portionof the screen decreases, thereby deteriorating a picture quality.

FIG. 3 is a graph illustrating the relationship between thetransmittance of the Fresnel lens sheet 10 and an incident angle oflight for the Fresnel lens sheet 10. Referring to FIG. 3, as theincident angle increases, the transmittance of the Fresnel lens sheet 10rapidly decreases. In the graph illustrated in FIG. 3, T1 denotes anamount of light passing through a plane incident surface 10 a of theFresnel lens sheet 10 shown in FIG. 2, T2 denotes an amount of lightpassing through an exit surface 10 b, i.e., a Fresnel lens surface, andTT denotes a product of T1 and T2.

As the light approaches the top of the screen, the incident angle oflight increases more significantly in a system shown in FIG. 2B(referred to as a second system) than in a system shown in FIG. 2A(referred to as a first system). Accordingly, referring to FIG. 3, thelight loss due to the reflection of light in the peripheral portion ofthe screen is greater in the second system than in the first system.

Consequently, when the light from an optical projection system 25 isobliquely incident onto a screen, as shown in FIG. 2B, a projectiondisplay can be made slim, but the picture quality deteriorates since adark area and a bright area occur on the screen.

SUMMARY OF THE INVENTION

The present invention has been made in view of the above-mentionedproblems. Accordingly, it is an aspect of the present invention toprovide a screen which has uniform luminance by evenly distributing thelight transmittance in the horizontal and vertical directions of thescreen, which further increases the light transmittance, and which makesa projection system slim.

To accomplish the aforementioned aspect, a screen for a projectiondisplay is provided. The screen includes a Fresnel lens sheet whichconverges light emitted from a light source and a lenticular lens sheetwhich disperses in a horizontal direction the light transmitted by theFresnel lens sheet. The Fresnel lens sheet includes a first Fresnel lenson one surface and a second Fresnel lens on an opposite surface.

The first Fresnel lens may further include a number of Fresnel lensunits. Each of these Fresnel lens units may include a first Fresnel lenssurface and a second Fresnel lens surface, where a first angle (of thefirst Fresnel lens surface with respect to a central line between thefirst and second Fresnel lens surfaces) and a second angle (of thesecond Fresnel lens surface with respect to the central line) arechanged according to the incident angles of the light.

To further solve the above-described problems, the first angle has arange of

${\frac{\pi}{2} - \alpha_{1}} \leq \theta_{1} \leq \frac{\pi}{2}$where θ₁ is the first angle and α₁ is a first incident angle of thelight with respect to a normal line of the screen.

Another aspect of the present invention provides a screen where eachFresnel lens unit is a total internal reflection prism.

Moreover, a condition of

$0 \leq {\theta_{2} - \frac{\pi}{2} + \left( {\theta_{1} + \theta_{2}} \right) - {\sin^{- 1}\left( {\sin\left( \frac{\alpha_{1} - \frac{\pi}{2} + \theta_{1}}{n_{2}} \right)} \right)}} \leq \frac{2\;\pi}{9}$is satisfied, where α₁ is a first incident angle of the light withrespect to a normal line of the screen, n₂ is a refractive index of amedium through which the light passes after being incident onto thefirst Fresnel lens surface, θ₁ is the first angle, and θ₂ is the secondangle.

Preferably, the first Fresnel lens and the screen are eccentric suchthat the center of the first Fresnel lens is below the center of thescreen.

The first Fresnel lens may also include two or more of the followingelements: a plate, a refraction prism, and a total internal reflectionprism based on the incident angles of light.

Preferably, the first Fresnel lens includes the plate in an area wherethe incident angle of light α₁ with respect to a normal line of thescreen, has a range of 0≦α₁<20, the refraction prism in an area where20≦α₁<50, and the total internal reflection prism in an area where50≦α₁≦80.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features and advantages of the present inventionwill become more apparent by describing in detail illustrative,non-limiting embodiments thereof with reference to the attached drawingsin which:

FIG. 1 is a perspective view of a conventional screen for a projectiondisplay;

FIG. 2A illustrates a conventional structure in which an opticalprojection system is disposed at the same level as the center of ascreen;

FIG. 2B illustrates another conventional structure in which an opticalprojection system is disposed below the screen;

FIG. 3 is a graph showing the relationship between the transmittance oflight and the incident angle of light in a conventional Fresnel lenssheet;

FIG. 4A is a perspective view of a screen for a projection display,according to a first illustrative, non-limiting embodiment of thepresent invention;

FIG. 4B is a side view of a Fresnel lens sheet employed in the screenaccording to the first embodiment of the present invention;

FIG. 5 is a partial enlarged view of a Fresnel lens employed in thescreen according to the first embodiment of the present invention;

FIG. 6 illustrates a relationship between the incident light and a prismunit of the Fresnel lens when the light is incident onto the Fresnellens employed in the screen according to the first embodiment of thepresent invention;

FIG. 7 is a graph comparing the light transmittance, according toincident position, between the screen according to the first embodimentof the present invention and the conventional screen; and

FIG. 8 illustrates a structure of a Fresnel lens employed in the screenaccording to a second illustrative, non-limiting embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE ILLUSTRATIVE, NON-LIMITING EMBODIMENTS OFTHE PRESENT INVENTION

The present invention will now be described in detail by describingillustrative, non-limiting embodiments thereof with reference to theaccompanying drawings. In the drawings, the same reference charactersdenote the same elements.

Referring to FIGS. 4A and 4B, a screen for a projection displayaccording to the first illustrative, non-limiting embodiment of thepresent invention includes a Fresnel lens sheet 40 and a lenticular lenssheet 55. The Fresnel lens sheet 40 includes a first Fresnel lens 42 onone surface and a second Fresnel lens 45 on an opposite surface. Thelenticular lens sheet 55 disperses in a horizontal direction lighttransmitted by the Fresnel lens sheet 40. The first and second Fresnellenses 42 and 45 may have their centers at the same level or at adifferent level as the center of the screen.

Referring to FIG. 5, the first Fresnel lens 42 includes a number ofridges. Each ridge is a a Fresnel lens unit. In other words, the firstFresnel lens 42 has a number of units 43. Each Fresnel lens unit 43 hasa first Fresnel lens surface 43 a and a second Fresnel lens surface 43b. FIG. 5 is an enlarged view of the first and second Fresnel lenssurfaces 43 a and 43 b included in the Fresnel lens unit 43. In FIG. 5,θ₁ denotes a first angle of the first Fresnel lens surface 43 a withrespect to a central line “c” between the first and second Fresnel lenssurfaces 43 a and 43 b, θ ₂ denotes a second angle of the second Fresnellens surface 43 b with respect to the central line “c”, α₁ denotes afirst incident angle with respect to a normal line of the screen, and α₂denotes a second incident angle with respect to a normal line of thesecond Fresnel lens surface 43 b. In this case, the second incidentangle α₂ can be expressed by Formula (1).

$\begin{matrix}{\alpha_{2} = {\alpha_{1} - \frac{\pi}{2} + \theta_{1}}} & (1)\end{matrix}$

In addition, n₁ denotes a refractive index of a first medium throughwhich the light passes before being incident onto the first Fresnel lens42, n₂ denotes a refractive index of a second medium through which thelight passes after being incident onto the first Fresnel lens 42, and βdenotes a refraction angle of the light after being incident onto thefirst Fresnel lens surface 43 a. Using these four values, Formula (2) isderived according to Snell's law.n ₁ sin α₂ =n ₂ sin β  (2)

In particular, when the refractive index of the first medium is 1, β isobtained by Formula (3).

$\begin{matrix}{\beta = {\sin^{- 1}\left( \frac{\sin\mspace{11mu}\alpha_{2}}{n_{2}} \right)}} & (3)\end{matrix}$

When the light refracted by the first Fresnel lens surface 43 a isfurther reflected by the second Fresnel lens surface 43 b, the angleformed between the second Fresnel lens surface 43 b and the reflectedlight is denoted by δ. In this case, δ can be derived using Formula (4).

$\begin{matrix}{\delta = {\frac{\pi}{2} + \beta - \left( {\theta_{1} + \theta_{2}} \right)}} & (4)\end{matrix}$

In addition, “m” denotes an incident angle or a reflection angle of thelight with respect to the second Fresnel lens surface 43 b and isobtained by Formula (5).

$\begin{matrix}{m = {\frac{\pi}{2} - \delta}} & (5)\end{matrix}$

When an angle between the normal line of the screen and the reflectedlight, i.e., an exit angle of the light with respect to the normal lineof the screen, is denoted by θ_(t), the exit angle θ_(t) can be definedusing θ₁, θ₃, and α₂ based on Formulae (4) and (5) as follows.

$\begin{matrix}\begin{matrix}{\theta_{t} = {\theta_{2} - \delta}} \\{= {\theta_{2} - \frac{\pi}{2} + m}} \\{= {\theta_{2} - \frac{\pi}{2} + \left( {\theta_{1} + \theta_{2}} \right) - {\sin^{- 1}\left( \frac{\sin\mspace{11mu}\alpha_{2}}{n_{2}} \right)}}}\end{matrix} & (6)\end{matrix}$

In addition, the exit angle θ_(t) can be defined using θ₁, θ₂, and α₁based on the Formula (1) as follows.

$\begin{matrix}{\theta_{t} = {\theta_{2} - \frac{\pi}{2} + \left( {\theta_{1} + \theta_{2}} \right) - {\sin^{- 1}\left( {\sin\left( \frac{\alpha_{1} - \frac{\pi}{2} + \theta_{1}}{n_{2}} \right)} \right)}}} & (7)\end{matrix}$

The first Fresnel lens 42 increases light transmittance throughout thescreen and also increases the uniformity of luminance throughout thescreen. In particular, as the incident angle of light α₁ with respect tothe normal line of the screen increases, the uniformity of luminancealso effectively increases.

To increase the light transmittance and the uniformity of luminance, thefirst angle θ₁ and the second angle θ₂ are changed according to avertical position on the screen. It is preferable that the first angleθ₁ and the second angle θ₂ satisfy the following conditions.

Firstly, referring to FIG. 3, the transmittance of light is over 90%when the incident angle is in a range from 0E to 30E. Accordingly, it ispreferable for the second incident angle α₂ with respect to the firstFresnel lens surface 43 a to have a range of 0≦α₂≦30. Based on thisfact, it is preferable for the second incident angle α₂ to have a rangeof 0≦α₂≦π/6 in order to decrease the amount of light reflected when thelight is incident onto the first Fresnel lens 42. The value of the firstangle θ₁ so as to allow the second incident angle α₂ to have thepreferable range, can be derived using Formula (1) as follows.

$\begin{matrix}\begin{matrix}{0 \leq {\alpha_{1} - \frac{\pi}{2} + \theta_{1}} \leq \frac{\pi}{6}} \\{{\frac{\pi}{2} - \alpha_{1}} \leq \theta_{1} \leq {{\frac{2}{3}\pi} - \alpha_{1}}}\end{matrix} & (8)\end{matrix}$

When the first angle θ₁ has a range defined by Formula (8) with respectto the first incident angle α₁, the first Fresnel lens 42 can obtain atransmittance of over 90%. In the meantime, since the first angle θ₁should be smaller than 90 degrees taking into account the usualstructure of a Fresnel lens, it is preferable that the first angle θ₁has a range of

${\frac{\pi}{2} - \alpha_{1}} \leq \theta_{1} \leq {\frac{\pi}{2}.}$

Secondly, it is preferable to determine the second angle θ₂ so as tominimize an area “f” of the first Fresnel lens surface 43 a onto whichthe light is not incident due to the second Fresnel lens surface 43 b.When the second angle θ₂ is greater than the first incident angle α₁,the light transmitted by the first Fresnel lens surface 43 a may not beincident onto the second Fresnel lens surface 43 b. Accordingly, it ispreferable that the second angle θ₂ is equal to or smaller than thefirst incident angle α₁ such that the light transmitted by the firstFresnel lens surface 43 a can be incident onto the second Fresnel lenssurface 43 b and then the light reflected by the second Fresnel lenssurface 43 b satisfies a third condition, i.e., total internalreflection, which will be described later. Considering theabove-described requirements, the second angle θ₂ can be defined byFormula (9). In FIG. 6, a reference character “e” denotes an area of thefirst Fresnel lens surface 43 a onto which the light is incident.θ₂≦α₁  (9)

Thirdly, it is preferable to subject the light to total internalreflection by the second Fresnel lens surface 43 b. The conditionexpressed by Formula (10) must be satisfied to subject the light tototal internal reflection by the second Fresnel lens surface 43 b.

$\begin{matrix}{m \geq {\sin^{- 1}\left( \frac{n_{1}}{n_{2}} \right)}} & (10)\end{matrix}$

Formula (10) provides a total internal reflection at the second Fresnellens surface 43 b. As a result, when n₁=1, Formula (10) can berearranged with respect to θ₁ and θ₂ using Formulae (4) and (5) asfollows.

$\begin{matrix}{{\sin^{- 1}\left\lbrack {\sin\left( \frac{\alpha_{1} - \frac{\pi}{2} + \theta_{1}}{n_{2}} \right)} \right\rbrack} \geq {\theta_{1} + \theta_{2} - {\sin^{- 1}\left( \frac{1}{n_{2}} \right)}}} & (11)\end{matrix}$

When the first and second angles θ₁ and θ₂ satisfy the above-describedtotal internal reflection condition, the Fresnel lens unit 43 can be atotal internal reflection prism. In addition, the first and secondangles θ_(l) and θ₂ of the Fresnel lens unit 43 change according to thefirst incident angle α₁.

Meanwhile, the exit angle θ_(t) of the first Fresnel lens 42 correspondsto an incident angle of the light onto the second Fresnel lens 45.Referring to FIG. 3, the second Fresnel lens 45 has a transmittance ofover 90% when the incident angle of light onto the second Fresnel lens45 is less than 30 degrees. However, taking into account the light lossat the first Fresnel lens 42, it is preferable for the exit angle θ_(t)of the first Fresnel lens 42 to have a range of 0≦θ_(t)≦20. As a result,the fourth condition is to have the exit angle θ_(t) satisfy theconditional expression 0≦θ_(t)≦20 using Formula (7).

It is preferable for the screen to have the first and second Fresnellens surfaces 43 a and 43 b with the first and second angles θ₁ and θ₂satisfy at least two of the above-described conditions. For example, theFresnel lens unit 43 may be formed having the first and second angles θ₁and θ₂ with respect to the first incident angle α₁ satisfy Formulae (8)and (9), or satisfying Formula (8) and having the exit angle θ_(t) in apredetermined range based on the Formula (7), or satisfying Formulae (9)and (10) or (11). When Formulae (8) and (9) are satisfied, the Fresnellens unit 43 functions as a refraction prism just refracting light. WhenFormulae (9) and (10) or (11) are satisfied, the Fresnel lens unit 43functions as a total internal reflection prism.

More preferably, the amount of light reflected by the first Fresnel lenssurface 43 a can be minimized by making α₂=0. When α₂=0, Formula (1) canbe rewritten as Formula (12).θ₁=90−α₁  (12)

Usually, the first incident angle α₁ has a range of about 0≦α₁≦80. Forexample, it is preferable that θ₁=30 when α₁=60 and θ₁=50 when α₁=40.

In addition, according to the Formula (10), when n₂=1.585, m≧39.11. Forexample, when m=40 and θ₂=60, the exit angle θ_(t) becomes 10 degreesaccording to the Formula (6).

As described above, when the first and second angles θ₁ and θ₂ changeaccording to the first and second incident angles α₁ and α₂ onto thefirst Fresnel lens surface 43 a, uniform light transmittance throughoutthe screen can be achieved even when the incident angle of light ontothe screen changes according to a vertical position on the screen. Inaddition, the amount of light can be increased throughout the screen. Inother words, the light transmittance can be increased in a portion of aconventional screen which typically has had a low transmittance, and anoverall amount of light and uniformity of luminance throughout thescreen can also be increased, by decreasing the incident angle θ_(t) oflight onto the second Fresnel lens 45 and equalizing incident angles ofthe light onto the second Fresnel lens 45 throughout the screen.

FIG. 7 is a graph of the relative luminance at various positions i.e., avertical position, on a quadrant I of the screen. In the graph shown inFIG. 7, a white bar indicates the light transmitted by a conventionalFresnel lens sheet, and a black bar indicates the light transmitted by aFresnel lens sheet according to the first, illustrative, non-limitingembodiment of the present invention. Referring to the graph, an amountof light increases throughout the screen, and uniformity of luminance isremarkably increased in the peripheral portion of the screen.

The first Fresnel lens 42 may be formed on either the incident surfaceor the exit surface of the Fresnel lens sheet 40. The second Fresnellens 45 may be a refraction Fresnel lens or a total reflection Fresnellens. When the first Fresnel lens 42 is formed on the incident surfaceof the Fresnel lens sheet 40, the second Fresnel lens 45 convergeslight, which has uniform exit angles due to the first Fresnel lens 42.When the first Fresnel lens 42 is formed on the exit surface of theFresnel lens sheet 40, light converged by the second Fresnel lens 45 isoutput at uniform angles due to the first Fresnel lens 42 so thatluminance is uniformly distributed throughout the screen.

In the first embodiment of the present invention, the screen is designedsuch that the first and second angles θ₁ and θ₂ are changed according tothe first and second incident angles α₁ and α₂. In this arrangement,since the first and second incident angles α₁ and α₂ change according tothe horizontal and vertical positions on the screen, the first andsecond angles θ₁ and θ₂ also change according to the horizontal andvertical positions on the screen. As a result, luminance is uniformlydistributed in both of the horizontal and vertical directions of thescreen.

The following description relates to a screen for a projection displayaccording to a second illustrative, non-limiting embodiment of thepresent invention.

The screen according to the second embodiment of the present inventionincludes a first Fresnel lens 50 and a second Fresnel lens 53. The firstFresnel lens 50 may have two or more of the following elements: a plate46, a refraction prism 47, and a total internal reflection prism 48depending on the incident angle of light. The second Fresnel lens 53 hasa refraction Fresnel lens. The reflection prism has surfaces 48 a and 48b.

The first Fresnel lens 50 includes a number of Fresnel lens unit, eachof which is implemented by the plate 46, the refraction prism 47, or thetotal internal reflection prism 48. For example, the first Fresnel lens50 may have the plate 46 in an area where an incident angle α₁ has arange of 0≦α₁<20, the refraction prism 47 in an area where an incidentangle α₁′ has a range of 20≦α₁′<50, and the reflection prism 48 in anarea where an incident angle α₁″ has a range of 50≦α₁″≦80.

Referring to FIG. 3, since the light transmission loss is small in thearea where the incident angle α₁ has the range of 0≦α₁<20, for themanufacturing efficiency, it is preferable to have the plate 46 as aFresnel lens unit in this area. When the light is incident onto theplate 46 at the incident angle α₁ having the range of 0≦α₁<20, if arefractive index n₁ of a first medium before the plate 46 is less than arefractive index n₂ of a second medium through which the light passesafter being incident onto the plate 46, a refraction angle (or an exitangle) θ_(t) of the light onto the plate 46 is less than the incidentangle α₁. Accordingly, the light passing through the plate 46 isincident onto the second Fresnel lens 53 at an angle of less than 20degrees.

It is preferable that the refraction prism 47, which satisfies Formulae(8) and (9), is used as a Fresnel lens unit when the incident angle α₁′has a range of 20≦α₁′<50. The refraction prism 47 has a first Fresnellens surface 47 a and a second Fresnel lens surface 47 b. A first angleof the first Fresnel lens surface 47 a with respect to a normal line ofthe screen is denoted by θ₁, and a second angle of the second Fresnellens surface 47 b with respect to the normal line of the screen isdenoted by θ₂. In this arrangement, the light incident onto the firstFresnel lens surface 47 a is set to output the light at the exit angleθ_(t) which is equal to or less than 20 degrees due to the refraction bythe first Fresnel lens surface 47 a.

When the incident angle α₁′ increases to be equal to or greater than 50degrees, the first angle θ₁ also increases. As a result, since a portionof the first Fresnel lens surface 47 a shaded by the second Fresnel lenssurface 47 b increases, an area of the first Fresnel lens surface 47 asubstantially decreases and an area of the second Fresnel lens surface47 b substantially increases. Accordingly, when a Fresnel lens unit isformed to have a uniform thickness, the size of the first Fresnel lenssurface 47 a performing refraction decreases and a reduction of the exitangle θ_(t) due to the refraction also decreases. Consequently, it ispreferable to use the refraction prism 47 when the incident angle α₁′ isless than 50 degrees and to use a prism of a type other than arefraction type when the incident angle α₁′ is greater than 50 degrees.

When the light is incident onto the refraction prism 47 at the incidentangle α₁′ having a range of 20≦α₁′<50, it is preferable that the secondangle θ₂ is less than the incident angle α₁ according to Formula (9). Inthis arrangement, it is preferable that an exit angle θ_(t)′ is equal toor less than 20 degrees. In this case, only refraction by the firstFresnel lens surface 47 a without total internal reflection by thesecond Fresnel lens surface 47 b is considered. The exit angle θ_(t)′can be defined using Snell's law as follows, assuming g that n₁=1.

$\begin{matrix}{\theta_{t}^{\prime} = {\frac{\pi}{2} - \theta_{1} - {\sin^{- 1}\left( {\sin\frac{\alpha_{1} - \frac{\pi}{2} + \theta_{1}}{n_{2}}} \right)}}} & (13)\end{matrix}$

A conditional expression for making the exit angle θ_(t)′ equal to orless than 20 degrees can be obtained using Formula (13) as follows.

$\begin{matrix}{0 \leq {\frac{\pi}{2} - \theta_{1} - {\sin^{- 1}\left( {\sin\frac{\alpha_{1} - \frac{\pi}{2} + \theta_{1}}{n_{2}}} \right)}} \leq 20} & (14)\end{matrix}$

When

${- 1} \leq {\sin\left\{ \left( {\alpha_{1} - \frac{\pi}{2} + \theta_{1}} \right) \right\}} \leq 1$and n₂ is about 1.5, the arcsin has a value ranging from −40 degrees to+40 degrees. When the arcsin is in the range of −40 to +40 degrees, thefirst angle θ₁ is obtained as follows.30≦θ₁≦50110≦θ₁≦130  (15)

Meanwhile, since the first angle θ₁ needs to be less than 90 degrees, itis preferable that the first angle θ₁ has the range of 30≦θ₁≦50 inFormula (15).

When the incident angle α₁″ has the range of 50≦α₁″≦80, the first andsecond angles θ₁ and θ₂ can be set to make the exit angle θ_(t)′ equalto or less than 20 degrees. When the incident angle α₁″ has the range of50≦α₁″≦80, it is preferable to use the total internal reflection prism48 as a Fresnel lens unit.

The first angle θ₁ is set to make a second incident angle α₂ zero inorder to minimize the reflection of light by the first Fresnel lens 50.When

${\alpha_{2} = 0},{\theta_{1} = {\frac{\pi}{2} - \alpha_{1}}}$according to the Formula (1). According to the Formula (3), β=0. Inaddition,

$m = {{\theta_{1} + \theta_{2}} = {\frac{\pi}{2} - \alpha_{1} + \theta_{2}}}$in Formula (5).

Next, when the total internal reflection condition, i.e., Formula (10),is satisfied, Formula (16) is derived.

$\begin{matrix}{\theta_{2} \geq {{\sin^{- 1}\left( \frac{1}{n_{2}} \right)} - \frac{\pi}{2} + \alpha_{1}}} & (16)\end{matrix}$

In this arrangement, it is assumed that n₁=1. For example, when acrylmedium having n₂=1.585 is used, θ₂>α₁−50.89. In addition, since thecondition of θ₂>0 needs to be satisfied, α₁″ needs to be set to greaterthan 50.89 degrees. When n₂=1.585, the condition of α₁″>50.89 issatisfied. In other words, the range of α₁″ can be changed based on thevalue of n₂.

Next, when an exit angle θ_(t)″ is set to have a range of 0≦θ_(t)″≦20using Formula (7), Formula (17) is derived.

$\begin{matrix}{\frac{\alpha_{1}^{''}}{2} \leq \theta_{2} \leq {10 + \frac{\alpha_{1}^{''}}{2}}} & (17)\end{matrix}$

As described above, when the incident angle α₁″ has the range of50≦α₁″≦80, the total internal reflection prism 48 is used as a Fresnellens unit and the first and second angles θ₁ and θ₂ change according tothe incident angle α₁″. In this arrangement, since the incident angleα₁″ changes in the horizontal and vertical directions of the screen, thefirst and second angles θ₁ and θ₂ also change according to a verticalposition and a horizontal position on the screen.

In addition, the first Fresnel lens 50 may have the refraction prism 47and the total internal reflection prism 48 according to the incidentangles. Alternatively, the first Fresnel lens 50 may have the plate 46and the refraction prism 47 depending on the incident angles.

As described above, a screen for a projection display according to theillustrative, non-limiting embodiments of the present invention hasFresnel lenses on the opposite surfaces of a Fresnel lens sheet. TheFresnel lens has a number of total internal reflection prisms whoseinternal angles are different according to the incident angles of light.Alternatively, the Fresnel lens may have two or more of the followingelements: a plate, a refraction prism, and a total internal reflectionprism, based on the incident angles of light. The Fresnel leans has theabove-described elements to obtain a uniform high luminance throughoutthe entire screen. In addition, the light obliquely incident onto ascreen in a slim projection display is compensated in both thehorizontal and vertical directions of the screen using a Fresnel lenssheet according to the illustrative, non-limiting embodiments of thepresent invention so that the luminance is uniformly or equallydistributed throughout the screen. As a result, the picture quality ofthe screen can be improved.

The above and other features of the invention including various andnovel details of the process and construction of the parts has beenparticularly described with reference to the accompanying drawings andpointed out in the claims. It will be understood that the particularprocess and construction of parts embodying the invention is shown byway of illustration only and not as a limitation of the invention. Theprinciples and features of this invention may be employed in varied andnumerous embodiments without departing from the scope of the invention.

1. A screen for a projection display, the screen comprising: a Fresnellens sheet operable to converge light emitted from a light source; and alenticular lens sheet operable to disperse in a horizontal direction thelight transmitted by the Fresnel lens sheet, wherein the Fresnel lenssheet comprises a first Fresnel lens on one surface and a second Fresnellens on an opposite surfaces, wherein the first Fresnel lens comprises aplurality of Fresnel lens units, each of the plurality of Fresnel lensunits comprises a first Fresnel lens surface and a second Fresnel lenssurface, wherein a first angle of the first Fresnel lens surface withrespect to a central line between the first and second Fresnel lenssurfaces, and a second angle of the second Fresnel lens surface withrespect to the central line, are changed depending on incident angles ofthe light, and wherein the first angle has a range of${\frac{\pi}{2} - \alpha_{1}} \leq \theta_{1} \leq \frac{\pi}{2}$ whereθ₁ is the first angle and α₁ is a first incident angle of the light withrespect to a normal line of the screen.
 2. The screen of claim 1,wherein the second angle satisfies a condition of θ₂=α₁ where θ₂ is thesecond angle and α₁ is a first incident angle of the light with respectto a normal line of the screen, and wherein when the condition issatisfied, there is minimized an amount of the light which is incidentonto the first Fresnel lens surface but is blocked by the second Fresnellens surface, is minimized.
 3. The screen of claim 1, wherein each ofsaid Fresnel lens units is a total internal reflection prism.
 4. Thescreen of claim 1, wherein a condition of$m \geq {\sin^{- 1}\left( \frac{n_{1}}{n_{2}} \right)}$ is satisfiedwhere “m” is an incident angle of the light onto the first Fresnel lenssurface, n₁ is a first refractive index of a medium through which thelight passes before being incident onto the second Fresnel lens surface,and n₂ is a second refractive index of a medium through which the lightpasses after being incident onto the first Fresnel lens surface.
 5. Thescreen of claim 1, wherein a condition of$0 \leq {\theta_{2} - \frac{\pi}{2} + \left( {\theta_{1} + \theta_{2}} \right) - {\sin^{- 1}\left( {\sin\left( \frac{\alpha_{1} - \frac{\pi}{2} + \theta_{1}}{n_{2}} \right)} \right)}} \leq \frac{2\;\pi}{9}$is satisfied where α₁ is a first incident angle of the light withrespect to a normal line of the screen, n₂ is a refractive index of amedium through which the light passes after being incident onto thefirst Fresnel lens surface, θ₁ is the first angle, and θ₂ is the secondangle.
 6. The screen of claim 1, wherein the first Fresnel lens has acenter at a different position from the second Fresnel lens.
 7. Thescreen of claim 6, wherein the first Fresnel lens and the screen areeccentric such that the center of the first Fresnel lens is below acenter of the screen.
 8. The screen of claim 1, wherein the firstFresnel lens comprises at least two of a plate, a refraction prism, anda total internal reflection prism based on incident angles of the light.9. The screen of claim 8, wherein the first Fresnel lens comprises: theplate in an area where the incident angle α₁ of the light with respectto a normal line of the screen has a first range of 0≦α₁<20, therefraction prism in an area where the incident angle α₁ of the lightwith respect to the normal line of the screen has a second range of20≦α₁<50, and the reflection prism in an area where the incident angleα₁ of the light with respect to the normal line of the screen has athird range of 50≦α₁≦80.
 10. The screen of claim 9, wherein therefraction prism satisfies a condition of$0 \leq {\frac{\pi}{2} - \theta_{1} - {\sin^{- 1}\left( {\sin\left( \frac{\alpha_{1} - \frac{\pi}{2} + \theta_{1}}{n_{2}} \right)} \right)}} \leq 20$where θ₁ is a first angle of one surface of the refraction prism withrespect to a central line of the refraction prism and θ₂ is a secondangle of the other surface of the refraction prism with respect to thecentral line.
 11. The screen of claim 8, wherein the total internalreflection prism satisfies a condition of$\theta_{1} = {\frac{\pi}{2} - \alpha_{1}}$ where θ₁ is a first angle ofone surface of the total internal reflection prism with respect to acentral line of the total internal reflection prism and α₁ is anincident angle of the light with respect to a normal line of the screen.12. The screen of claim 11, wherein a condition of$\theta_{2} \geq {{\sin^{- 1}\left( \frac{1}{n_{2}} \right)} - \frac{\pi}{2} + \alpha_{1}}$is satisfied, where θ₂ is a second angle of a second surface of thetotal reflection prism with respect to the central line, and n₂ is arefractive index of a medium through which the light passes after beingincident onto the first Fresnel lens.
 13. The screen of claim 8, whereineach of the refraction prism and the total internal reflection prismcomprises a first angle and a second angle with respect to a centralline of the prism, and the first angle and the second angle change basedon the incident angles of the light.
 14. The screen of claim 1, whereinthe second angle satisfies a condition of θ₂≦α₁, where θ₂ is the secondangle, and α₁ is a first incident angle of the light with respect to anormal line of the screen, and wherein when the condition is satisfied,there is minimized an amount of the light which is incident onto thefirst Fresnel lens surface but is blocked by the second Fresnel lenssurface.
 15. The screen of claim 1, wherein the Fresnel lens sheet andthe lenticular lens sheet are adjacent to each other without any otherintervening components.